3. $100 $200 $300 $400 $500 $200 $300 $400 $500 Parallel Lines and Transversals Angles and Parallel Lines Distance Equations of Lines Proving Lines are Parallel

4. Parallel Lines and Transversals for $100 Define: Skew lines

5. Answer Skew Lines - Lines that are not coplanar and do not intersect Back

6. Parallel Lines and Transversals for $200 Define: Parallel Lines

7. Answer Parallel Lines – Lines that are coplanar and do not intersect. Back

8. Parallel Lines and Transversals for $300 Define: Transversal

9. Answer Transversal – A line that intersects two or more lines in a plane at different points Back

10. Parallel Lines and Transversals for $400 Name all the line segments parallel to AB

11. Answer Back CD, GH, EF

12. Parallel Lines and Transversals for $500 Name all of the line segments perpendicular to GC

13. Answer Back EG, GH, CA, CD

14. Angles and Parallel Lines for $100 Identify two pairs of consecutive interior angles in the following drawing given l || m: l m n 14 23 58 6 7

15. Answer <4 and <5, <3 and <6 Note: <4 + <5 = 180 degrees Back l m n 14 23 58 6 7

16. Angles and Parallel Lines for $200 Identify two pairs of corresponding angles in the following drawing given l || m: l m n 14 23 58 6 7

17. Answer 1 and 5, 4 and 8, 2 and 6, 3 and 7 NOTE: 1 5 Back l m n 14 23 58 6 7

18. Angles and Parallel Lines for $300 Identify two pairs of alternate interior angles in the following drawing given l || m: l m n 14 23 58 6 7

19. Answer <4 and <6, <3 and <5 Note: <4 <6 Back l m n 14 23 58 6 7

20. Angles and Parallel Lines for $400 Given r is parallel to t, find the measure of angle 6

21. Answer Back <2 = 135 degree angle – corresponding angles. <2 and < 6 are supplementary 135 + < 6 = 180 <6 = 45 degrees

22. Angles and Parallel Lines for $500 m<1 = 6x, and m<3 = 7x - 20. Find the value of x for p to be parallel to q. The diagram is not to scale.

23. Answer Back m<1 must be congruent to m<3 for p || q 6x = 7x – 20 20 = x

24. Equations of Lines for $100 Write the equation of the line in slope-intercept form: The line with a slope of -5 through point (-2, -4)

25. Answer Point: (-2, -4) m = -5 Slope-intercept Form: y = mx + b -4 = -5(-2) + b -4 = 10 + b -14 = b Thus, y = -5x - 14 Back

26. Equations of Lines for $200 Write the equation of the line in slope-intercept form: The line through points (-2, 3) and (0, -1)

27. Answer Point: (-2, 3) Point: (0, -1) m = (y 2 – y 1 )/(x 2 – x 1 ) m = (-1- 3)/(0 – -2) = -4/2 = -2 Slope-intercept Form: y = mx + b -1 = -2(0) + b -1 = b Thus, y = -2x - 1 Back

28. Equations of Lines for $300 Write the equation of the line in point-slope form: The line through points (2, -3) and (-2, 3)

29. Answer Points: (2, -3) and (-2, 3) m = (y 2 – y 1 )/(x 2 – x 1 ) m = (3- -3)/(-2 – 2) = 6/-4 = -3/2 Point-Slope Form: y – y 1 = m(x – x 1 ) where (x 1, y 1 ) is a point on the line Thus, the equation of the line is y – 3 = -3/2(x - -2) y – 3 = -3/2(x + 2) Back

30. Equations of Lines for $400 Write the equation of a line perpendicular to the given line that intersects the given line on the y-axis. Write your answer in point-slope form: y = 3x - 8

31. Answer y = 3x – 8 So, m = 3, a point on the line = (0,-8) Point-Slope Form: y – y 1 = m(x – x 1 ) y - -8 = 3(x – 0) y + 8 = 3x Slope of the Perpendicular line: (-1/3) y + 8 = (-1/3)x Back

32. Equations of Lines for $500 Graph the following line: y = 3x - 2

33. Answer 3x - 2 Back

34. Proving Lines to be Parallel for $100 Which 2 lines are parallel? a) 5y = -3x - 5 b) 5y = -1 – 3x c) 3y – 2x = -1

35. Answer Back Writing the lines in slope-intercept form: a) 5y = -3x – 5 y = (-3/5)x – 1 b) 5y = -1 – 3x y = (-3/5)x – (1/5) c) 3y – 2x = -1 3y = 2x – 1 y = (2/3)x – (1/3) a||b

36. Proving Lines to be Parallel for $200 Given: <3 is supplemental to <8 Prove: p || r

37. Answer Back StatementsReasons <3 is supplemental to <8Given <3 + <8 = 180Def. of Supplemental angles <3 + <4 = 180Def of Supplementary angles <4 is congruent to <8Theorem: Two angles supplementary to the same angle are congruent <4 and <8 are corresponding angles Definition of corresponding angles p || rTheorem: If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel

38. Proving Lines to be Parallel for $300 Given: <1 is congruent to <5 Prove: p || r

39. Answer Back StatementsReasons <1 is congruent to <5 Given <4 is congruent to <1 Vertical Angles <4 <1 and <1 <5 thus, <4 <5 Transitive property of angle congruence Thus, p || r Theorem: If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel

40. Proving Lines to be Parallel for $400 Suppose you have four pieces of wood like those shown below. If b = 40 degrees can you construct a frame with opposite sides parallel? Explain.

41. Answer Back No, they are different transversals, so there is no theorem to prove the sides are congruent

42. Proving Lines to be Parallel for $500 Write a paragraph proof of this theorem: In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. Given: r is perpendicular to s, t is perpendicular to s Prove: r || t

43. Answer By the definition of perpendicular, r ┴ s implies m<2 = 90, and t ┴ s implies m<6 = 90. Line s is a transversal. <2 and <6 are corresponding angles. By the Converse of the Corresponding Angles Postulate, r || t. Back

44. Distance for $100 Define: Distance between lines

45. Answer Distance between lines: the shortest distance between the two lines Back

46. Distance for $200 Given that two lines are equidistance from a third line, what can you conclude?

47. Answer The two lines are parallel to each other Back

48. Distance for $300 Define: equidistant

49. Answer Equidistant: The distance between two lines measured along a perpendicular line to the lines is always the same. Back

50. Distance for $400 What are the steps to find the distance between two parallel lines?

51. Answer Back 1)Write both lines in slope-intercept form 2)Find the equation of a line perpendicular to the two parallel lines 3)Find the intersection of the perpendicular line with each of the given two lines 4)Find the distance between the two points

52. Distance for $500 Find the distance between the given parallel lines y = 2x – 3 2x – y = -4

53. Answer Back d = √(9.8) (See Homework Solution Online)